A total of 12,000 children under 13 filled the Juventus stadium at the weekend to watch the Serie A game against Udinese.
The club's initiative, which was applauded by many, prevented Sunday's game from being played behind closed doors.
Juve had been handed a stadium closure for that match as punishment for their fans' geographically discriminatory chants towards Napoli supporters in last month's game.
A statement from the Lega Serie A read: "Juventus have been fined 5000 euros for their very young supporters having repeatedly insulted a player of a rival team."
Brkic made a number of fine saves throughout the game before Fernando Llorente scored the winner in stoppage time to hand Juve a 1-0 triumph.
The win lifted Juve three points clear at the top of Serie A.